1. Field of the Invention
The present invention relates generally to inertial navigation systems, and specifically to a system and method for improving the accuracy of pressure altitude determinations in an inertial navigation system.
2. Description of Related Art
Inertial navigation systems in aircrafts have typically employed accelerometers to provide position information to a navigation computer. It is well known that the vertical position (altitude) of the aircraft can be determined from a measured acceleration in the vertical direction by performing a double time integration of the measured vertical acceleration.
The double integration of acceleration in the vertical direction is unstable as acceleration bias can lead to exponential growth in the computed altitude, causing the estimated altitude calculation to have unbounded error due to several factors. First, any vertical acceleration measurement errors from the accelerometers are directly integrated in subsequent calculations to cause both vertical velocity and vertical position error. Second, in order to obtain the actual value for vertical acceleration from the measurement taken by the accelerometer, the effects of gravity must be subtracted from the vertical acceleration measurement. Erroneous acceleration measurements will cause incorrect values for gravity to be subtracted from the measured acceleration, which further compounds the error in the altitude determination causing an even faster growth in the altitude error. Thus, inertial navigation systems relying upon the integration of acceleration measurements to obtain an estimation of altitude are unstable systems.
To provide a more stable inertial navigation system, external references have been used either alone or in combination with inertial measurements to compute estimations of altitude. For instance, a barometric altimeter is a well known device for providing altitude information as a function of the value of barometric pressure based on the direct relationship between pressure and altitude. Barometric altitude, also known as pressure altitude, is determined as a function of pressure based on the standard day model for the atmosphere: ##EQU1##
where S is the pressure altitude, K.sub.1 =44.342 [km], K.sub.2 =0.190263 [km], K.sub.3 =45.395 [km], K.sub.4 =14.605 [km], P.sub.0 =1013.25 [mb], and P.sub.B =226.32 [mb]. Since the barometric altitude determination is stable, it is typically used in a variety of mechanizations to aid or bound the altitude estimations computed from the inertial measurements in the inertial vertical loop. The independent pressure altitude estimation that aids the inertial vertical loop is referred to as the slave altitude.
Differences between the altitude estimation and true altitude can result from the altitude estimation being based on the standard atmosphere, whereas actual atmospheric conditions encountered by a navigation system are usually nonstandard. Furthermore, errors in the sensors providing the intertial vertical loop data and the pressure data used for the altitude estimation will produce differences between the actual altitude and the estimated altitude. These errors have been modeled in a five state Kalman filter mechanization for the free inertial vertical loop in order to minimize their detrimental effects, as described in the article "A Kalman Filter Mechanization for the Baro-Inertial Vertical Channel" by J. Ausman in Proceedings of the Institute of Navigation Forty Seventh Annual Meeting, Williamsburg, Va., pp. 153-159, 1991. The disclosure of this article is hereby incorporated by reference into the present application. This Kalman filter mechanization models five error states including three error states for the inertial vertical loop (inertial vertical acceleration error, inertial vertical velocity error, and inertial vertical position error) and two error states for the pressure altitude (barometric scale factor and barometric bias in the barometer).
The barometric bias and barometric scale factor estimate errors in the pressure altitude determinations made from pressure measurements taken by the barometric altimeter. The barometric bias and scale factor error states essentially attempt to account for differences between the calculated pressure altitude and the calculated intertial altitude, so that the barometic scale factor and the barometric bias are actually modeling errors in altitude. However, the barometric altimeter does not directly measure altitude, rather it directly measures pressure and then mathematically converts the pressure measurement to a value for altitude. Thus, barometric scale factor and barometric bias are actually modeling altitude errors in the barometric altimeter in an artificial domain, since these error states are modeling errors in altitude instead of modeling errors in the actual pressure measurements taken. Noise and pressure offsets in the pressure sensor will result in erroneous pressure measurements which are, in turn, converted into erroneous altitude determinations. The effects of noise and offset on the pressure sensor offset error can deviate substantially at higher altitudes from purely an altitude error, so that merely modeling altitude errors will not always provide an accurate correction of the altitude determination.
Thus, there is clearly a need for a system and method for directly modeling the pressure sensor offset error and noise in the pressure measurements themselves in order to increase the accuracy of altitude determinations in an inertial navigation system.